Abstract

We study solutions of the surface quasi-geostrophic (SQG) equation which are locally constant outside a thin neighbourhood of a curve that evolves with time. To such an SQG solution we associate a distinguished curve (the 'spine'). If the above thin neighbourhood has thickness delta, then we prove that the spine satisfies its own evolution equation (equal to the sharp-front equation) modulo errors O(delta(2) | log delta|).